S-05-22
•
?
SIMON FRASER UNIVERSITY
Senate Committee on University Priorities
?
Memorandum
TO: Senate
RE:
Curriculum Changes: Department
of Mathematics
FROM: ?
John Waterh
Chair, SCUP
Vice-Preside Academic
DATE:
?
January 21,i20
At its January 12, 2005 meeting the Senate Committee on University Priorities (SCUP)
recommended the following motion:
Motion
That Senate approve and recommend to the Board of Governors the proposal for
program changes to the MSc Program in the Department of Mathematics."
end.
C:
J. Driver
P. Mustard
I. Chen
G. Nicholls
S
S
SIMON FRASER UNIVERSITY
?
DEAN OF GRADUATE STUDIES
?
MEMORANDUM
TO: ?
SCUP
FROM: ?
Jonathan Driver, Dean of Graduate Studies
SUBJECT: Curriculum changes: Department of Mathematics
DATE: ?
7th
December 2004
cc: ?
Peter Mustard, Chair, Faculty of Science Graduate Program Committee;
I. Chen, Chair, Department of Mathematics Graduate Program Committee
At its 6
th
December 2004 meeting Senate Graduate Studies Committee unanimously
approved the enclosed proposal for curriculum changes in the Department of
Mathematics. Because this proposal involves significant structural changes to the MSc
program, I am forwarding this to SCUP for approval, rather than to Senate for
information.
I would like to draw your attention to three points.
First, for many years the Department of Mathematics has included in its Calendar entry
the statement that graduate students may fulfil some of the departmental course
requirements (but not the University's minimum requirements) by taking some 400 level
undergraduate courses. This practice will now be changed. Courses taken by graduate
students in conjunction with undergraduate students will receive a separate number at the
700 level. As a result, there are a large number of new course proposals included in this
package, as well as a number of necessary editorial changes to the Calendar. There are a
number of advantages to this change. For example, the Calendar will reflect the topics
that are taught at the graduate level, and the requirements for graduate students taking
700 level courses can be differentiated from the requirements for undergraduate students
taking the 400 level courses.
Second, the Department of Mathematics has introduced a project option. This has
necessitated the addition of a number of new courses.
Third, a number of courses will be dropped from the Calendar. I have asked the
Department of Mathematics to send a list of these courses directly to SCUP.
o ?
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1.
GS200436
p
SIMON FRASER UNIVERSITY
?
MEMORANDUM
To: ?
J. Driver, ?
From:
M. Plischk
Dean of Graduate Studies
?
Faculty of
NOV 082004
e
DN OF GRADUATE
S ien9UDIES OFFICE
.
Subject: ?
Faculty of Science Graduate
?
Date:
November 5, 2004
Curriculum
The following items have been approved by the Faculty of Science and are forwarded for
approval by the Senate Graduate Studies committee. Please include these on the next SGSC
agenda.
EEE2)
Change to Applied Mathematics Program
Changes to the Mathematics Graduate Program
* New courses: MATH 701-4, MATH 716-3, MATH 718-3, MATH 719-3, MATH 724-3, MATH
725-3,
MATH 738-3, MATH 739-3, MATH 740-3, MATH 743-3, MATH
745-3,
MATH 747-4, MATH 761-3, MATH 762-3, MATH 767-3, MATH 817-4, MATH 818-4,
MATH 842-4, MATH 843-4, MATH 845-4, MATH 878-0, MATH 879-0, MATH 880-6 and
MATH 882-0
** Course Changes: APMA
935-4,
MATH 814-4, MATH 820-4 and MATH 821-4
*/**
DETAILED COURSE PROPOSALS/ COURSE REVISION'INFORMATION
AVAILABLE FOR RE'
S
JIEW BY
CONTACTING BOBBIE GRANT, SENATE ASSISTANT AT
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b7.
604 291-3168 OR EMAIL bgrant@sfu.ca
•
?
?
M. Plischke
c. P. Mustard, Chair, Faculty of Science Graduate Studies Committee
.
.
a.
Memorandum
To: ?
John Waterhouse, SCUP
CC: ?
Jon Driver
From: Imin Chen, MATH GSC
Date:
?
1/4/2005
Re: ?
List of courses to be deleted in the revisions to the Mathematics
Graduate Program
To whom it may concern:
Upon the request of Jon Driver, this is a clarification to the proposal to revise the Mathematics
Graduate Program which is on route from the SGSC to the SCUP. Courses listed in the current
calendar entry for the Mathematics Program which are not listed in the proposed calendar entry for
the Mathematics Program are to be deleted from the program, namely, the following courses:
MATH 806-4 Mathematical Logic II
MATH 807-4 Mathematical Logic: Selected Topics
MATH 808-4 Mathematical Logic III
MATH 812-4 Algebra!
MATH 813-4 Algebra II
MATH 815-4 Algebra III
MATH 816-4 Algebra IV
MATH 825-4 Enumeration
MATH 832-4 Real Analysis II
MATH 837-4 Complex Analysis II
MATH 839-4 Topology I
Yours truly,
MATH 840-4 Topology II
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Imin Chen
MATH GSC
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Revisions to the Mathematics Graduate Program Calendar Entries
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Ml
Mathematics Graduate Program: Proposed Revision
This document describes a proposed revision of the calendar entry for the
graduate program in mathematics.
The primary purpose of this revision is to bring the list of graduate courses found
in the calendar in line with what we normally and expect to offer on a regular
basis. In addition, we are taking the opportunity to introduce a number of
changes to improve the graduate program.
1.
a new project course MSc degree
2.
the introduction of 7xx courses which may be offered in conjunction with a
4xx course
3.
appropriate revisions to the MSc and PhD degree requirements
In addition to this document, the following paperwork is appended in support of
the proposal:
1.
For each new course number introduced, a completed New Course
Approval Cover Sheet and a New Graduate Course Proposal Form
(MATH 701, MATH 716, MATH 718, MATH 719, MATH 724, MATH 725,
MATH 738, MATH 739, MATH 740, MATH 743, MATH 745, MATH 747,
MATH 761, MATH 762, MATH 767, MATH 817, MATH 818, MATH 842,
MATH 843, MATH 845, MATH 878, MATH 879, MATH 880, MATH 882).
2.
A library assessment for the new courses introduced.
3.
For each revision to a course in the current calendar, a completed Course
Change Form (MATH 814, MATH 820, MATH 821)
.
/7
Revisions to the Mathematics Graduate Program Calendar Entries
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Implementation Remarks:
1. Due to the number of changes to the program and the complexity of possible
situations which may arise, the GSC will initially send out a memo on a regular
basis which will give its official interpretation of the degree requirements. This
includes clarifications on such issues as areas of mathematics, course selection,
etc. Once a fairly standard set of interpretations is established, these may be
incorporated into a further revision of the calendar entries at a future date.
2 The 7xx courses
are categorized as graduate courses which may be offered in
conjunction with a 4xx course. Normally more stringent course requirements will
be imposed on graduate students taking such a co-offered course. There is a
limit in the degree requirements on the number of such courses taken..
3.
In order to address the issue of increased difficulty with the presence of
graduate students, changes are being sought in the mathematics major program
(not the honours program) to reduce the number of 4xx courses required while
increasing the breadth of 3xx courses required. The situation will, be monitored
and changes introduced as necessary.
4.
Courses in the old calendar which are not in the new calendar will be deleted
from the program.
5.
The program is designed so that students are not forced at the very start to
decide which MSc option they would like to take.
6.
The final examination MATH 882 for the course work MSc will be examined by
an examination committee to be formed by two faculty members and held every
semester. This will be a pass/fail course.
7.
Guidelines for grading of the project course MATH 880 will be included in the
GSC memo mentioned above. The passing grade will be the minimum pass
grade for a graduate course (i.e. a C).
Revisions to the Mathematics Graduate Program Calendar Entries
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M3
This proposal was approved at the departmental meeting held on 20 October
2004.
(1
I. -
Chen, Chair of MATH GSC
22 October 2004
.
.
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Revisions to the Mathematics Graduate Program Calendar Entries
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Change from:
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Change to:
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Mathematics ?
Mathematics
r
MSc Program Requirements
A candidate normally obtains at least 20
credit hours beyond courses taken for the
bachelor's degree. Of these, at least 12 are
graduate courses or seminars, and the
remaining eight may be from graduate
courses or seminars or 400 division
undergraduate courses. The student
must also submit a satisfactory thesis and
will attend an oral examination based on that
thesis and related topics.
Note:
APMA 900-990 (page 387) and STAT
800-890 (page 398) may be used to satisfy
requirements for the master of science
degree.
MSc Program Requirements (Thesis
Option)
A MSc candidate is normally required to
complete at least 18 graduate credit hours
beyond courses taken for the applicant's
bachelor's degree. Of these, at least 12
credits should be from courses numbered
800 or above. The course work should
normally involve at least two different areas
of mathematics subject to the approval of
the student's supervisory committee and the
department's graduate studies committee.
The candidate is also required to submit a
satisfactory thesis and defend it at an oral
examination based on the thesis and related
topics (MATH 898).
See "Graduate General Regulations" on
page 308 for further information and
regulations.
MSc Program Requirements (Project
Course Option)
?
-
A MSc candidate is normally required to
complete at least 30 graduate credit hours
beyond courses taken for the applicant's
bachelor's degree. Of these, at least 18
credits should be from courses numbered
800 or above. The course work should
normally involve at least three different
areas of mathematics subject to the
approval of the student's supervisory
committee and the department's graduate
studies committee.
The candidate is required to take and pass
the project course MATH 880 and the
examination course MATH 882. At most one
unsuccessful attempt each at MATH 880
and at MATH 882 is allowed.
See "Graduate General Regulations" on
page 308 for further information and
regulations.
0
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Revisions to the Mathematics Graduate Program Calendar Entries
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Change from:
PhD Program Requirements
A candidate will generally obtain at least 28
credit hours beyond those for the bachelor's
degree. Of these, at least 16 are graduate
courses or seminars and the remaining 12
may be graduate courses, seminars or 400
level undergraduate courses. Students with
an MSc in mathematics or statistics are
deemed to have earned 12 of the 16 hours
and eight of the 12 undergraduate or
graduate hours required. Course work in all
cases will involve study in at least four
different areas of mathematics and/or
statistics.
Candidates will normally pass a two stage
general exam. The first stage covers a
broad range of senior undergraduate
material. In the second, students present to
their supervisory committee a written thesis
proposal and then defend this at an open
oral defence. The supervisory committee
evaluates the thesis proposal and defence
and either passes or fails the student. A
candidate ordinarily cannot take either stage
of the general examination more than twice.
Both stages must be completed within six
full time semesters of initial enrolment in the
PhD program.
The supervisory committee may require
proficiency in reading mathematical papers
in either French, German or Russian.
Students must submit and successfully
defend a thesis which embodies a significant
contribution to mathematical knowledge.
See "Graduate General Regulations" on
cLe 308 for further information and
regulations.
Note: APMA 900-990 (g
g
e 387) and STAT
800-890 (pa
g
e 9) may be satisfy PhD
requirements.
Change to:
PhD Program Requirements
A PhD candidate is normally required to
complete the MSc requirements (either
option) and at least 12 further graduate
credit jours. Of these, at least 8 credits
should be from courses numbered 800 or
above. Subject to the approval of the
department's graduate studies committee, a
PhD candidate with a MSc is deemed to
have completed the MSc requirements for
the purposes of the PhD program
requirements. The graduate course work
should normally involve at least four different
areas of mathematics subject to the
approval of the Student's supervisory
committee and the department's graduate
studies committee.
Candidates will normally be required to pass
a two stage general exam. The first stage
consists of successful completion of a
comprehensive examination (MATH 878). In
the second, students present to their
supervisory committee
a
written thesis
proposal and then defend this at an open
oral defence (MATH 879). The supervisory
committee evaluates the thesis proposal and
defence and either passes or fails the
student. A candidate cannot take either
stage of the general examination more than
twice. Both stages must be completed within
six full time semesters of initial enrolment in
the PhD program.
Students must submit and successfully
defend a thesis which embodies a significant
contribution to mathematical knowledge
(MATH 899).
See "Graduate General Regulations" on
page 308 for further information and
regulations.
S
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Revisions to the Mathematics Graduate Program Calendar Entries
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Change from:
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Change to:
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Mathematics Graduate Courses
MATH 601-4 Discovering
Mathematics I
Arithmetic and Geometry form the core of
the elementary school curriculum. The
fundamental concepts in both these areas of
mathematics will be approached through
exploratory exercises and problems as well
as in projects. The students will work both
singly and in groups to explore the ideas of
mathematics. The presentations will be non-
theoretical. Prerequisite: acceptance into the
master's program in mathematics education
or permission of the department. Graduate
students in Department of Mathematics
cannot take this course to satisfy their
degree requirements.
MATH 602-4 Discovering Mathematics II
Discrete mathematics is used in computer
communications, scheduling and
transportation problems. Statistics is
encountered by each of us every day in the
newspapers and on television as medical
findings, sporting results and economic
strategies are discussed. These are two of
the most accessible areas of modem
applied mathematics and many problems
and the ideas behind their solution can be
understood and appreciated by students
with only a modest mathematical
background. Several topics in these areas
and their relationship to real world problems
will be explored. The exploration will be
done through a series of projects with
students often working in teams and making
presentations of their discoveries. The
presentation will be non-theoretical.
Prerequisite: MATH 601 and acceptance
into the master's program in mathematics
education or permission of the department.
Graduate students in Department of
Mathematics cannot take this course to
satisfy their degree requirements.
Mathematics Graduate Courses
MATH 601-4 Discovering Mathematics I
Arithmetic and Geometry form the core of
the elementary school curriculum. The
fundamental concepts in both these areas of
mathematics will be approached through
exploratory exercises and problems as well
as in projects. The students will work both
singly and in groups to explore the ideas of
mathematics. The presentations will be non-
theoretical. Prerequisite: acceptance into the
master's program in mathematics education
or permission of the department. Graduate
students in Department of Mathematics
cannot take this course to satisfy their
degree requirements.
MATH 602-4 Discovering Mathematics Il
Discrete mathematics is used in computer
communications, scheduling and
transportation problems. Statistics is
encountered by each of us every day in the
newspapers and on television as medical
findings, sporting results and economic
strategies are discussed. These are two of
the most accessible areas of modern
applied mathematics and many problems
and the ideas behind their solution can be
understood and appreciated by students
with only a modest mathematical
background. Several topics in these areas
and their relationship to real world problems
will be explored. The exploration will be
done through a series of projects with
students often working in teams and making
presentations of their discoveries. The
presentation will be non-theoretical.
Prerequisite: MATH 601 and acceptance
into the master's program in mathematics
education or permission of the department.
Graduate students in Department of
Mathematics cannot take this course to
satisfy their degree requirements.
0
Revisions to the Mathematics Graduate Program Calendar Entries
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Change from:
MATH 603-4
Foundations of Mathematics
Crises in mathematics, their historical and
philosophical background and their
resolution. Prerequisite: acceptance into the
MSc program in mathematics education or
permission of the department. Graduate
students in the Department of Mathematics
cannot take this course to satisfy their
degree requirements.
MATH 604-4 Geometry
Euclidean and non-Euclidean geometries.
Klein's erlangen program. Prerequisite:
entrance into the MSc in mathematics
education program or permission of the
department. Graduate students in the
Department of Mathematics cannot take this
course to satisfy their degree requirements.
MATH 605-4 Mathematics in Context
Mathematical modeling in the largest sense
with a focus on topics and issues related to
doing and discovering mathematics,
including explorations of available
computational resources, e.g. Maple.
Prerequisite: acceptance into the MSc
program in mathematics education and one
year of university level calculus. Graduate
students in the Department of Mathematics
cannot take this course to satisfy their
degree requirements.
Change to:
MATH 603-4 Foundations of Mathematics
Crises in mathematics, their historical and
philosophical background and their
resolution. Prerequisite: acceptance into the
MSc program in mathematics education or
permission of the department. Graduate
students in the Department of Mathematics
cannot take this course to satisfy their
degree requirements.
MATH 604-4 Geometry
Euclidean and non-Euclidean geometries.
Klein's Erlangen program. Prerequisite:
entrance into the MSc in mathematics
education program or permission of the
department. Graduate students in the
Department of Mathematics cannot take this
course to satisfy their degree requirements.
MATH 605-4 Mathematics in Context
Mathematical modeling in the largest sense
with a focus on topics and issues related to
doing and discovering mathematics,
including explorations of available
computational resources, e.g. Maple.
Prerequisite: acceptance into the MSc
program in mathematics education and one
year of university level calculus. Graduate
students in the Department of Mathematics
cannot take this course to satisfy their
degree requirements.
.
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Revisions to the Mathematics Graduate Program Calendar Entries
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MS
S
Change to:
* 700 division courses may be offered in
conjunction with a 400 division course.
Students may not take a 700 division course
if it is being offered in conjunction with a 400
division course which they have taken
previously.
MATH 701-4 Computer Algebra
Data-structures and algorithms for
mathematical objects, including polynomials,
general mathematical formulae, long integer
arithmetic, polynomial greatest common
divisors, the Risch integration algorithm.
Other topics include symbolic differentiation,
simplification of formulae, and polynomial
factorization. Students will learn Maple for
use on assignments.
MATH 716-3 Numerical Analysis II
The numerical solution of ordinary
differential equations and elliptic, hyperbolic
and parabolic partial differential equations
will
be considered.
MATH 718-3 Partial Differential Equations
First-order linear equations, the method of
characteristics. The wave equation.
Harmonic functions, the maximum principle,
Green's functions. The heat equation.
Distributions and transforms. Higher
dimensional eigenvalue problems. An
introduction to nonlinear equations. Burgers'
equation and shock waves.
MATH 719-3 Linear Analysis
Convergence in Euclidean spaces, Fourier
series and their convergence, Legendre
polynomials, Hermite and Laguerre
polynomials.
MATH 724-3 Applications of Complex
Analysis
Conformal mapping, application to boundary
value problems, Schwarz-ChriStOffel
transformation, integral formulas, analytic
continuation, argument principle.
MATH 725-3 Real Analysis
Metric spaces, normed vector spaces,
measure and integration, an introduction to
functional analysis.
.
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Change from:
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(1
Revisions to the Mathematics Graduate Program Calendar Entries
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-
MATH 738-3 Linear-Algebra
Linear Algebra. vector space and matrix
theory.
MATH 739-3 Algebraic Systems
Algebraic systems including, for example,
groups, rings. Polynomial theory.
MATH 740-3 Galois Theory
An introduction to the theory of fields, with
emphasis on Galois theory.
MATH 743-3 Combinatorial Theory
Graph colouring, Hamiltonian graphs, planar
graphs, random graphs, Ramsey theory,
extremal problems, additional topics.
MATH 745-3 Graph Theory
Graph colouring, Hamiltonian graphs, planar
graphs, random graphs, Ramsey theory,
extremal problems, additional topics.
MATH 747-4 Coding Theory
An introduction to the theory and practice of
error-correcting codes. Topics will include
finite fields, polynomial rings, linear and non-
linear codes, BCH codes, convolutional
codes, majority logic decoding, weight
distribution of codes, and bounds on the size
of codes.
MATH 761-3 Continuous Mathematical
Models
Formulation, analysis and numerical solution
of continuous mathematical models.
Applications may be selected from topics in
physics, biology, engineering and
economics.
MATH 762-3 Fluid Dynamics
Incompressible fluid flow phenomena:
kinematics and equations of motion, viscous
flow and boundary layer theory, potential
flow, water waves. Aerodynamics.
MATH 767-3 Dynamical Systems
Stability and bifurcation in vector fields and
discrete maps. Centre manifold theory and
applications of normal forms. Introduction to
chaos, Lyapunov exponents, and normal
hyperboliCitY.
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Revisions to the Mathematics Graduate Program Calendar Entries
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SChange from:
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Change to:
MATH 800-4
Pure Mathematics: Selected
?
MATH 800-4 Mathematics: Selected
Topics ?
Topics
MATH 806-4
Mathematical Logic II
First-order theories. Some syntactical
theorems concerning provability, such as the
equivalence and equality theorems; the
completeness theorem and some of its
consequences for equivalence of syntactical
and semantical notions, and introduction to
model theory; incompleteness of formal
arithmetic.
MATH 807-4
Mathematical Logic:
Selected Topics
MATH 808-4
Mathematical Logic Ill
Introduction to recursion theory. Church's
Thesis, Godel-Rosser incompleteness
theorem, undecidability. Kleen's normal form
theorem and enumerations theorem, the
recursion theorem. The arithmetic hierarchy,
the analytical hierarchy. Degrees of
•
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urisolvability. Basic theorems. Additional
topics, if time permits. Prerequisite: MATH
806.
MATH 812-4 Algebra I
Theory of fields. Topics covered will include
separable, normal, Galois, and
transcendental extensions; finite fields and
algebraically closed fields. Additional topics
may include infinite Galois groups, valuation,
Kummer extensions and Galois
cohomology, further material in algebraic
number theory.
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Revisions to the Mathematics Graduate Program Calendar Entries
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Change from.
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0
MATH 813-4 Algebra II
Group theory. Generators and relations,
normalizers and centralizers, composition
series. Permutation groups, Sylow theory,
abelian groups. Other topics covered will be
the theory of p-groups, nilpotent and
solvable groups, and some aspects of
simple groups.
MATH 814-4 Algebra: Selected Topics
MATH 815-4 Algebra
Ill
Rings and modules. Commutative and
noncornmutative associate rings with
ascending or descending chain condition.
Jacobson radical Chevalley-Jacobson
density theorem, Wedderburn-Artifl
theorems, Goldie theorems, with
applications to matrix groups and group
algebras. As time permits, homological and
MATH 817-4 Groups and Rings
local methods.
A survey of graduate group and/or ring
theory. Possible topics include generators
MATH 816-4 Algebra IV
and relations, composition series, Sylow
Homology. Categories, functors, adjoint
theory, permutation groups, abelian groups,
functors, homology, and cohomology of a
complex. Universal coefficient theorem; Extn
p-groups, nilpotent and solvable groups,
aspects of simple groups, representation
cohomology of groups; Schurs theorem.
theory, group algebras, chain conditions,
Tensor and torsion products. Global
Jacobson radical, Chevalley-Jacobson
dimension of rings,
density theorem, Wedderburn-Artin
theorems.
MATH 818-4 Algebra and Geometry
An introduction to algebraic geometry with
supporting commutative algebra. Possible
topics include Hilbert basis theorem,
Hilbert's Nullstellensatz, Groebner bases,
ideal decomposition, local rings, dimension,
tangent and cotangent spaces, differentials,
varieties, morphisms, rational maps, non-
singularity, intersections in projective space,
cohomology theory, curves, surfaces,
homological algebra.
MATH 819-4 Algebra: Selected Topics
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Revisions to the Mathematics Graduate Program Calendar Entries
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?
Change to:
MATH 820-4 Graph Theory
A first graduate course in graph theory
dealing with some of the following: algebraic
graph theory, extremal graph theory,
coloring problems, applications of graphs,
hypergraphs, and current research topics.
MATH 821-4 CombinatoricS
An introduction to the theory of block
designs, finite geometries and related topics
MATH 820-4 Graph Theory
Algebraic graph theory, extremal graph
theory, colouring problems, path and cycle
structure of graphs, application of graphs,
hypergraphs, and current research topics.
MATH 821-4 Combinatorics
An introduction to the theory of incidence
structures (finite geometries, block designs)
and their relation to linear codes. Algebraic
techniques - finite group actions, orbit
enumeration, generation of orbit
representatives. Exact and asymptotic
enumeration of labelled and unlabelled
structures.
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Revisions to the Mathematics Graduate Program Calendar Entries
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.
Change from:
MATH 825-4 Enumeration
Enumeration problems concerned with
permutations, sequences, partitions, lattice
walks and graphs, algebraic and analytic
properties of generating functions,
asymptotic analysis.
MATH 826-4 Posets and Matroids
An introduction to the theory of posets,
geometric lattices and matroids.
MATH 827-4 Discrete Mathematics:
Selected Topics
MATH 831-4 Real Analysis I
An intensive study of Lebesque measure,
integration and the Lebesque convergence
theorems together with the treatment of
such topics as absolute continuity, the
fundamental theorem of calculus, the Lp-
spaces, comparison of types of convergence
in function spaces, the Baire category
theorem.
MATH 832-4 Real Analysis II
This course normally covers abstract
measure and integration, and material which
collectively might be called an introduction to
functional analysis (e.g. complete metric
spaces, normal spaces, the Stone-
Weierstrass theorem, linear functionals and
the Hahn-Banach theorem). Other
specialized topics in modern analysis.
Prerequisite: MATH 831.
MATH 833-4 Analysis: Selected Topics
Change to:
MATH 826-4 Posets and Matroids
An introduction to the theory of posets,
geometric lattices and matroids.
MATH 827-4 Discrete Mathematics:
Selected Topics
MATH 831-4 Real Analysis I
An intensive study of Lebesque measure,
integration and the Lebesque convergence
theorems together with the treatment of
such topics as absolute continuity, the
fundamental theorem of calculus, the Lp-
spaces, comparison of types of convergence
in function spaces, the Baire category
theorem.
MATH 833-4 Analysis: Selected Topics
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0
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Change from:
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Change to:
.
MATH 836-4 Complex
Analysis I
Topics covered normally will include:
Riemann surfaces, complex conjugate co-
ordinates; the maximum principle, boundary
value problems; conformal mappings,
Schwartz-ChriStOffel formula; the symmetry
principle, analytic continuation.
MATH 837-4 Complex
Analysis
II
Topics covered will include some of the
following: entire functions, normal families,
Hubert space of analytic functions;
conformal mappings of special functions;
Picard's theorem. Prerequisite: MATH 836.
MATH 839-4 Topology I
A first graduate course in general topology,
dealing with some of the following topics:
set-theoretic preliminaries, topological
spaces, filters and nets, connectedness
notions, separation properties, countability
properties, compactness properties,
paracompactneSS, metrization, uniform
spaces, function spaces.
MATH 840-4 Topology II
A second graduate course in general
topology dealing with additional topics
among those listed for MATH 839.
Prerequisite: MATH 839.
MATH 841-4 Topology: Selected Topics
MATH 836-4 Complex
Analysis I
Topics covered normally will include:
Riemann surfaces, complex conjugate co-
ordinates; the maximum principle, boundary
value problems; conformal mappings,
Schwartz-ChristOffel formula; the symmetry
principle, analytic continuation.
MATH 841-4 Topology: Selected Topics
MATH 842-4 Algebraic Number Theory
Review of Galois theory, integrality, rings of
integers, traces, norms, discriminants,
ideals, Dedekind domains, class groups, unit
groups, Minkowski theory, ramification,
cyclotomic fields, valuations, completions,
applications.
MATH 843-4 Analytic and Diophantine
Number Theory
Arithmetical functions, distribution of prime
numbers, theory of Dirichlet characters,
Dirichiet series, theory of Riemann Zeta
functions and Dirichiet L-functions,
exponential sums, character sums,
Diophantine equations, Diophantine
approximations. applications.
MATH 845-4 Number Theory: Selected
Topics
.
ii.
Revisions to the Mathematics Graduate Program Calendar Entries
?
M15
Change from:
?
Change to:
MATH 877-1 Supplementar
y
Reading ?
MATH 877-1 SupplenefltarY Reading
MATH 878-0 PhD Comprehensive
Examination
A comprehensive written examination
covering a broad range of senior
undergraduate and graduate material.
MATH 879-0 PhD Thesis Proposal
An open oral defence of a written thesis
proposal presented to the student's
supervisory committee.
MATH 880-6 MSc Project
A project leading to research in mathematics
completed under the supervision of a faculty
member. The project will consist of a written
report and a public presentation. This course
can only be used for credit towards the MSc
project course option.
MATH 882-0 MSc Final Examination
A written examination covering senior
undergraduate and basic graduate material.
S
9
Revisions to the Mathematics Graduate Program Calendar Entries
?
M16
Change from:
MATH 890-0 PracticUm I
First semester of work experience in a co-
operative education program. (0-0-0)
MATH 891-0 PracticUm II
Second semester of work experience in a
co-operative education program. (0-0-0)
MATH 892-0 Practicum III
Third semester of work experience in the
Co-operative Education Program. (0-0-0)
Prerequisite: MATH 891.
MATH 893-0 Practicum IV
Fourth semester of work experience in the
Co-operative Education Program. (0-0-0)
Prerequisite MATH 892.
MATH 894-2 Reading
MATH 895-4 Reading
MATH 896-2 Introductory Seminar
MATH 897-2 Advanced Seminar
MATH 898-0 MSc Thesis
MATH 899-0 PhD
Thesis
Change to:
MATH 890-0 PractiCUm I
First semester of work experience in a co-
operative education program. (0-0-0)
MATH 891-0 PractiCum II
Second semester of work experience in a
co-operative education program. (0-0-0)
MATH 892-0 PracticUm III
Third semester of work experience in the
Co-operative Education Program. (0-0-0)
Prerequisite: MATH 891.
MATH 893-0 Practicum IV
Fourth semester of work experience in the
Co-operative Education Program.
(0-0-0) Prerequisite: MATH 892.
MATH 894-2 Reading
MATH 8954 Reading
MATH 896-2 Introductory Seminar
MATH 897-2 Advanced Seminar
MATH 898-6 MSc Thesis
MATH 899-6 PhD Thesis
* The credit values assigned to MATH 898
and MATH 899 are for administrative
purposes only and cannot be used towards
degree course work requirements.
I'?.
GS2004362
Memo: Modified Calendar Entry for Graduate Applied Math Program
1 Rationale
With the cross-listing of fourth year courses at the 700-level students could take undergraduate courses to fulfill graduate
course requirements. This was not the intention of the program, so we propose that the following be added to the calendar
entry: "Normally courses that are cross-listed as undergraduate courses cannot be used to satisfy graduate level course
requirements."
Furthermore, it is sometimes the case that students take courses that are credited at 3-credit hours (eg, 400 level under-
graduate courses and graduate courses outside of mathematics). To take this into account, the total requirement for credit
hours should be dropped to 26 credit hours.
2 Proposed Calendar Entry
A candidate for the MSc will normally be required to obtain a total of 26 credit hours beyond courses taken for the bachelor's
degree. These 26 hours will consist of at least four courses chosen from the list of core courses below with at least one course
from each of the pairs APMA 900,901; APMA 920, 922; APMA 930, 935; a further seven credit hours at the graduate level;
and a further three credit hours which may be at the graduate level or at the 400 undergraduate level. Normally courses
that are cross-listed as undergraduate courses cannot be used to satisfy graduate level course requirements. The six core
courses are
APMA 900-4 Advanced Mathematical Methods I
APMA 901-4 Advanced Mathematical Methods II
APMA 920-4 Numerical Linear Algebra
APMA 922-4 Numerical Solution of Partial Differential Equations
APMA 930-4 Fluid Dynamics
APMA 935-4 Analysis and Computation of Models
In addition to this course requirement (normally completed in five semesters), the student completes a project which
involves a significant computational component and submits and successfully defends a project report. This project should
be completed within about one semester.
3 Current Calendar Entry
A candidate for the MSc will normally be required to obtain a total of 28 credit hours beyond courses taken for the bachelor's
degree. These 28 hours will consist of at least four courses chosen from the list of core courses below with at least one course
from each of the pairs APMA 900,901; APMA 920, 922; APMA 930, 935; a further eight credit hours at the graduate level;
and a further four credit hours which may be at the graduate level or at the 400 undergraduate level. The six core courses
are
APMA 900-4 Advanced Mathematical Methods I
APMA 901-4 Advanced Mathematical Methods II
APMA 920-4 Numerical Linear Algebra
APMA 922-4 Numerical Solution of Partial Differential Equations
APMA 930-4 Fluid Dynamics
APMA 935-4 Mechanics of Solids
In addition to this course requirement (normally completed in five semesters), the student completes a project which
involves a significant computational component and submits and successfully defends a project report. This project should
be completed within about one semester.
0
